Negotiating the Probabilistic Satisfaction of Temporal Logic Motion Specifications

We propose a human-supervised control synthesis method for a stochastic Dubins vehicle such that the probability of satisfying a specification given as a formula in a fragment of Probabilistic Computational Tree Logic (PCTL) over a set of environmental properties is maximized. Under some mild assumptions, we construct a finite approximation for the motion of the vehicle in the form of a tree-structured Markov Decision Process (MDP). We introduce an efficient algorithm, which exploits the tree structure of the MDP, for synthesizing a control policy that maximizes the probability of satisfaction. For the proposed PCTL fragment, we define the specification update rules that guarantee the increase (or decrease) of the satisfaction probability. We introduce an incremental algorithm for synthesizing an updated MDP control policy that reuses the initial solution. The initial specification can be updated, using the rules, until the supervisor is satisfied with both the updated specification and the corresponding satisfaction probability. We propose an offline and an online application of this method.Comment: 9 pages, 4 figures; The results in this paper were presented without proofs in IEEE/RSJ International Conference on Intelligent Robots and Systems November 3-7, 2013 at Tokyo Big Sight, Japa

On the Minimal Revision Problem of Specification Automata

As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the requirements are expressed as temporal logic specifications. However, in real-life scenarios, it is to be expected that not all user task requirements can be realized by the robot. In such cases, the robot must provide feedback to the user on why it cannot accomplish a given task. Moreover, the robot should indicate what tasks it can accomplish which are as "close" as possible to the initial user intent. This paper establishes that the latter problem, which is referred to as the minimal specification revision problem, is NP complete. A heuristic algorithm is presented that can compute good approximations to the Minimal Revision Problem (MRP) in polynomial time. The experimental study of the algorithm demonstrates that in most problem instances the heuristic algorithm actually returns the optimal solution. Finally, some cases where the algorithm does not return the optimal solution are presented.Comment: 23 pages, 16 figures, 2 tables, International Joural of Robotics Research 2014 Major Revision (submitted

Vehicle control from temporal logic specifications with probabilistic satisfaction guarantees

Thesis (Ph.D.)--Boston UniversityTemporal logics, such as Linear Temporal Logic (LTL) and Computation Tree Logic (CTL), have become increasingly popular for specifying complex mission specifications in motion planning and control synthesis problems. This dissertation proposes and evaluates methods and algorithms for synthesizing control strategies for different vehicle models from temporal logic specifications. Complex vehicle models that involve systems of differential equations evolving over continuous domains are considered. The goal is to synthesize control strategies that maximize the probability that the behavior of the system, in the presence of sensing and actuation noise, satisfies a given temporal logic specification. The first part of this dissertation proposes an approach for designing a vehicle control strategy that maximizes the probability of accomplishing a motion specification given as a Probabilistic CTL (PCTL) formula. Two scenarios are examined. First, a threat-rich environment is considered when the motion of a vehicle in the environment is given as a finite transition system. Second, a noisy Dubins vehicle is considered. For both scenarios, the motion of the vehicle in the environment is modeled as a Markov Decision Process (MDP) and an approach for generating an optimal MDP control policy that maximizes the probability of satisfying the PCTL formula is introduced. The second part of this dissertation introduces a human-supervised control synthesis method for a noisy Dubins vehicle such that the expected time to satisfy a PCTL formula is minimized, while maintaining the satisfaction probability above a given probability threshold. A method for abstracting the motion of the vehicle in the environment in the form of an MDP is presented. An algorithm for synthesizing an optimal MDP control policy is proposed. If the probability threshold cannot be satisfied with the initial specification, the presented framework revises the specifica- tion until the supervisor is satisfied with the revised specification and the satisfaction probability is above the threshold. The third part of this dissertation focuses on the problem of stochastic control of a noisy differential drive mobile robot such that the probability of satisfying a time constrained specification, given as a Bounded LTL (BLTL) formula, is maximized. A method for mapping noisy sensor measurements to an MDP is introduced. Due to the size of the MDP, finding the exact solution is computationally too expensive. Correctness is traded for scalability, and an MDP control synthesis method based on Statistical Model Checking is introduced